Nonlinear Optimal Control Theory [Hardcover]

Nonlinear Optimal Control Theorypresents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas.

Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also discusses Hamilton-Jacobi theory. By providing a sufficient and rigorous treatment of finite dimensional control problems, the book equips readers with the foundation to deal with other types of control problems, such as those governed by stochastic differential equations, partial differential equations, and differential games.

Examples of Control Problems
Introduction
A Problem of Production Planning
Chemical Engineering
Flight Mechanics
Electrical Engineering
The Brachistochrone Problem
An Optimal Harvesting Problem
Vibration of a Nonlinear Beam

Formulation of Control Problems
Introduction
Formulation of Problems Governed by Ordinary Differential Equations
Mathematical Formulation
Equivalent Formulations
Isoperimetric Problems and Parameter Optimization
Relationship with the Calculus of Variations
Hereditary Problems

Relaxed Controls
Introduction
The Relaxed Problem; Compact Constraints
Weak Compactness of Relaxed Controls
Filippovs Lemma
The Relaxed Problem; Non-Compact Constraints
The Chattering Lemma; Approximation to Relaxed Controls

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